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Mirrors > Home > ILE Home > Th. List > ancld | GIF version |
Description: Deduction conjoining antecedent to left of consequent in nested implication. (Contributed by NM, 15-Aug-1994.) (Proof shortened by Wolf Lammen, 1-Nov-2012.) |
Ref | Expression |
---|---|
ancld.1 | ⊢ (φ → (ψ → χ)) |
Ref | Expression |
---|---|
ancld | ⊢ (φ → (ψ → (ψ ∧ χ))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | idd 21 | . 2 ⊢ (φ → (ψ → ψ)) | |
2 | ancld.1 | . 2 ⊢ (φ → (ψ → χ)) | |
3 | 1, 2 | jcad 291 | 1 ⊢ (φ → (ψ → (ψ ∧ χ))) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 97 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia3 101 |
This theorem is referenced by: mopick2 1980 cgsexg 2583 cgsex2g 2584 cgsex4g 2585 reximdva0m 3230 difsn 3492 preq12b 3532 elres 4589 relssres 4591 fnoprabg 5544 1idprl 6566 1idpru 6567 msqge0 7400 mulge0 7403 fzospliti 8802 |
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